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On the Bishop-Phelps-Bollobas theorem for multilinear mappingsopen access
- Issue Date
- 1-Nov-2017
- Publisher
- ELSEVIER SCIENCE INC
- Keywords
- Bishop-Phelps theorem; Bishop-Phelps-Bollobas property; Norm attaining; Bilinear forms
- Citation
- LINEAR ALGEBRA AND ITS APPLICATIONS, v.532, pp 406 - 431
- Pages
- 26
- Indexed
- SCI
SCIE
SCOPUS
- Journal Title
- LINEAR ALGEBRA AND ITS APPLICATIONS
- Volume
- 532
- Start Page
- 406
- End Page
- 431
- ISSN
- 0024-3795
1873-1856
- Abstract
- We study the Bishop-Phelps-Bollobas property and the Bishop-Phelps-Bollobas property for numerical radius. Our main aim is to extend some known results about norm or numerical radius attaining operators to multilinear and polynomial cases. We characterize the pair (l(1)(X), Y) to have the BPBp for bilinear forms and prove that on L-1(mu) the numerical radius and the norm of a multilinear mapping are the same. We also show that L-1(mu) fails the BPBp-nu for multilinear mappings although L-1(mu) satisfies it in the operator case for every measure mu. (c) 2017 Elsevier Inc. All rights reserved.
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Related Researcher
- Lee, Han Ju
- College of Education (Department of Mathematics Education)